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Question
Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.
Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.
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Solution
The steps for construction for a tangent from a point outside the circle are:
a) Draw a line segment from P to the centre of the circle O and bisect it. Let it be at a point, say M.
b) With PM as radius draw a circle. Let this circle intersect the initial circle at points X and Y
c) Join PX and PY. They are the required tangents.
Since PO is the diameter of the new circle, X and Y are 90∘ ( Angles in a semicircle)
But OX and OY are radii of the circle.
Any line that makes a right angle with radii is a tangent to a circle.
Hence, PX and PY have to be tangents to the circle.
The steps for construction for a tangent from a point outside the circle are:
a) Draw a line segment from P to the centre of the circle O and bisect it. Let it be at a point, say M.
b) With PM as radius draw a circle. Let this circle intersect the initial circle at points X and Y
c) Join PX and PY. They are the required tangents.
Since PO is the diameter of the new circle, X and Y are 90∘ ( Angles in a semicircle)
But OX and OY are radii of the circle.
Any line that makes a right angle with radii is a tangent to a circle.
Hence, PX and PY have to be tangents to the circle.
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